Recent mid-infrared interferometry observations of nearby active galactic nuclei (AGN) revealed that a significant part of the dust emission extends in the polar direction, rather than the equatorial torus/disk direction as expected by the traditional unification model. We study the X-ray signatures of this polar dusty gas with ray-tracing simulations. Different from those from the ionized gas, the scattered emission from the polar dusty gas produces self-absorption and neutral-like fluorescence lines, which are potentially a unique probe of the kinematics of the polar dusty gas. The anomalously small Fe Kα/Si Kα ratios of type II AGN observed previously can be naturally explained by the polar dusty gas, because the polar emission does not suffer from heavy absorption by the dense equatorial gas. The observed Si Kα lines of the Circinus galaxy and NGC 1068 show blue-shifts with respect to the systemic velocities of the host galaxies, consistent with an outflowing scenario of the Si Kα-emitting gas. The 2.5-3 keV image of the Circinus galaxy is elongated along the polar direction, consistent with an origin of the polar gas. These results show that the polar-gas-scattered X-ray emission of type II AGN is an ideal objective for future X-ray missions, such as Athena.